
V.^UTER K . WILMB] 




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LIBRARY OF CONGRESS. 



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DNITED STATES OP AMERICA. 



ME0HANI0AL Drawing, 



PROJECTION DRAWING. 

ISOMETRIC AND OBLIQUE DRAWING. 

WORKING DRAWINGS. 



A CONDENSED TEXT FOR CLASS ROO 





WALTER K. PALMER, M. E., 

(OHIO STATE UNIVERSITY) 

Department of Drawing, Miller Manual Labor School, 
cro^et, virginia. 






Columbus, Ohio : 

c h a s . b . p a l m e k , 

i'uhlishek. 



Ai^ 



Copyright, 1894, by 
SALTER K. PALMER. 



[A/^ rights reserved.\ 



CONTENTS, 



PAGE. 

Introduction ii 

PROJECTION DRAWING. 

Principles of Projection. page. 

General Discussion 13 

Fundamental Ideas of Projection 13 

Application to Drawing 14 

Notation 17 

General Principles 19 

Points ig 

Lines 19 

Surfaces and Solids 19 

Point of Sight 20 

Orthographic Projection 20 

Scenographic Projection — Perspective 20 

Drawing. 

Conventional Lines 21 

Exercise 22 

Projections of a Point 22 

Plate I 22 

Projections of Lines 22 

Projections of Right Lines 23 

Principles 23 

Plate II 24 

Revolution 25 

Of a Point 25 

Principles 25 

Plate III 26 



IV CONTEXTS. 

PAGE, 

Of Lines 26 

True Length 26 

Angles with H and V 26 

Plate IV • 27 

Plate V 27 

Projection and Revolution 27 

Of Plane Figures 27 

Plate VI 28 

Plate VII ■ 28 

Of Solids 28 

Plate VIII 28 

Shade Lines 29 

Conventional Direction of Light • 29 

Definition of Shade Lines 29 

Exercise 30 

Projection 30 

Of Pyramid Cylinder and Cone 30 

Plate IX 30 

Of Sphere and Ellipsoid 30 

Plate X 30 

Third Projection 30 

Plate XI 31 

ISOMETRIC AXD OBLIQUE. 

Isometric. page. 

Definition 35 

Isometric Projection 35 

Isometric Drawing 36 

Isometric Axes 36 

Isometric Lines 37 

Use of Co-ordinates 37 

Example 11 

Shade Lines 38 

Direction of Light 39 

Plate XII 39 

Plate XIII : 39 



CONTENTS. V 

Oblique. page. 

How Differing from Isometric 40 

Shade Lines 40 

Cabinet Perspective 40 

Plate XIV 40 

Plate XV 40 



WORKINCx DRAWINGS. 

Working Drawings. page. 

Defined 43 

How Made 43 

The Three Views 43 

Sections 43 

Cross Sectioning 44 

General Rules 45 

Shade Lines 45 

Drawing to Scale 46 

Dimensioning 46 

Dimension Line 46 

Center Line 47 

Isometric and Oblique for Working Drawings 47 

General Views and Details 48 

Details 48 

How Made 48 

Indexing 49 

Conclusion , 49 



PREFilGE. 



The followinf^" pag"es contain the substance of a pro- 
gressive course, beg'inning" with the essential principles 
of elementary Projection Drawing, and passing on as 
rapidly as is consistent with thoroughness, through 
Isometric and Oblique Drawing, to the making of 
ivorkmg drawing's. 

The work is simply outlined, briefly, for the conveni- 
ence of teacher and students. Explanations and illus- 
trations by the teacher will be needed, and the course 
may be supplemented or modified by him, as the needs 
of a particular class may seem to require. 

The little book is meant to be simply a "teacher's 
help," — a text strictly. It is, however, not a text, 
such as the usual text books on Mechanical Drawing. 
It embodies a general method of instruction. The aim 
is to assist the student in developing for himself the 
essential fundamental principles, in a natural and pro- 
gressive order, starting with the most elementary 
ideas, and working along by easy steps from one fact 
to another, until the whole subject is unfolded. 

The principles are in most cases simply stated. The 
student should thoroughly verify each in order, with 
the assistance of the teacher when necessary. Explan- 
ations and illustrations are not given, for each state- 
ment follows directly and easily from what has just 
preceded it, and it is one of the chief benefits of the 
work, to verify the statements given and make simple 
sketches and models to illustrate them. 



8 PREFACE. 

By little helps in the way of hints and illustrations, 
and by questioning- to recall facts already established, 
any student may be led to develop for himself all the 
essential principles of the subjects treated, in such a 
way that he cannot well forget them. At the same 
time he acquires the habit of working- from a know- 
ledg-e of principles, — of thinking- and reasoning-, and 
relying- on what he knows. 

The plates g-iven are chosen to illustrate the princi- 
ples brought out. Coming as they do at the close of 
each topic, after the principles have been established, 
they bring those principles into use, and fix the method 
of their application, thus preparing for the next step. 

No drawings are shown, and as few figures as pos- 
sible are used, as it is expected that the teacher will 
supply what is needed to clear up individual difficul- 
ties, and that he will develop the actual work of draw- 
ing, in the class room, by little helps and suggestions. 

It is left altogether with the teacher as to what shall 
be drawn under the head of "Working Drawings." 
It is well to draw from measurements taken directly 
from objects, or from sketches taken from machine 
details. Shop exercises in a technical school afford 
good practice. Revising a set of badly made shop 
drawings, is good training. The work should be 
arranged as progressively as possible. 

Considerable practice should be given in making the 
general drawing-s of complete machines, and detailing 
from them; also in detailing from drawings made by 
others; after which a course in designing may properly 
be given. 

A scheme for tabulating and indexing the details, 
should be arranged by the student when he makes a 
general drawing of a machine, and this should be fol- 
lowed by those who detail from his drawing. 



PREFACE. 9 

It will be necessar}^ for the teacher to supply much 
relating" to working* drawings, in the way of conven- 
tional methods of doing* various thing's, such, for in- 
stance, as representing" screw threads, drawing" hexago- 
nal bolt heads, etc. Such things are best given to 
students individually, as they are ready to make use 
of them. There are many little "ways" that must 
be broug"ht out by the teacher, as the need for them 
occurs. He will of course draw upon standard works 
of reference, his own experience, and reliable examples 
of practice. Students should be frequently referred 
to books by g"ood authorities, and to shop drawing"s 
from the drafting" rooms of leading" machine works, 
manufacturing companies and railroad shops. 

Great pains should be taken to have thorougfhly g-ood 
drawing's made. Accuracy, neatness and correctness 
should be insisted upon. With proper attention to de- 
tails, really fine work can be obtained from average 
students. 

A standard size of plate is recommended, until the 
working" drawings are reached. A small size of plate 
is preferable, as working" on a small drawing* is found 
to enforce accuracy. "Freedom" can be quickly ac- 
quired when the student comes to a larg"e drawing*. If 
too much " freedom " be allowed at first, accuracy will 
never be acquired. 

Only the very best paper should be used. A stand- 
ard plate of Keuffel & Esser's "normal" paper, 
6| X 8^ ", with a border line \ " from the edge all 
around, has proved very satisfactory. 

Working" drawings should be penciled upon ordinary 
"detail paper," then traced upon g-ood tracing* cloth, 
and blue prints made from the tracings, if time allows. 

When the student is done, the exercises and plates, 



10 PREFACE. 

and the working drawings he has made, which should 
be thoroughly good work, and can easily be, with 
proper attention on the part of the teacher, make with 
the text a complete work upon the subject. Thus the 
student helps to make for himself a work of reference 
for his permanent use, and while so doing becomes 
thoroughly grounded in the principles and practices of 
the work. 

The method is not only natural and systematic, but 
trial in the class room proves that it arouses and main- 
tains the interest of the student, and eventually pro- 
duces the most satisfactory results in the way of know- 
ledge and skill acquired, and training in systematic 
work and study. 

It is assumed that the student is reasonably skillful 
in the use of instruments before taking up this course, 
and it should be preceded by a thoroughly good course 
in Geometric Construction Drawing. A previous in- 
troduction into Geometry is necessar3% as a knowledge 
of the terms and definitions of Geometry is assumed. 

W. K. P. 

Crozet, Va., April, 1894. 



MECHANICAL DRAWING. 



INTRODUGTION. 

1. Mechanical Drawing is the art of making- drawing's 
capable of representing- mechanical and architectural 
structures, and the parts composing- them, so clearly 
and completely that skilled mechanics can make those 
structures exactly as they are intended to be, without 
any further directions than those contained in the 
drawing-s themselves. 

2. Such drawing-s made expressly for the workmen 
are called " Working Drawings." 

3. Evidently, these drawing-s, to meet the require- 
ments, must express easily and perfectly all facts in 
reg-ard to the f>ositio)i^ form and magnitude of objects 
represented. 

4. In other words, they must be capable of express- 
ing- the g'eometry of all mathematical fig-ures, — solid as 
well as plane, — for Geometry is defined as "that branch 
of mathematics which treats of position^ form and 
mag'nititdey 

5. They must represent these solid figures i)i space^ 
yet the drawing's must all be in one plane — that of the 
paper. 

6. It is evident, that the art of Mechanical Drawing- 
must have as its foundation an exact mathematical 
science. This is the science of " Projections." 

11 



12 MECHANICAL DRAWING. 

7. Drawing's made in accordance with the methods 
of Projection Drawing-, meet all requirements com- 
pletely. 

RBVIBW QUESTIONS. 



1. What is meant by Mechanical Drawing? 

2. What are "Working drawings?" 

3. What are the requirements to be met by working drawings ? 

4. What is the definition of Geometry ? 

5. What is the distinction between an art and a science ? 

6. Is Mechanical Drawing a science or an art ? Or is it both ? 

7. What is the foundation of Mechanical Drawing ? 

8. How are the requirements of Mechanical Drawing met ? 



PROJEGTION DR:HWING. 



PRINCIPLES OF proj:ection. 

8. Projection Drawing is tbe science and art of produc- 
ing- drawings which shall represent completely all facts 
of position, form and mag^nitude of all geometrical 
quantities in space. 

9. The Methods employed in Projection Drawing-, are 
those of " Orthographic Projection," which is the basis of the 
science of Descriptive Geometry, 

FUNDAMENTAI< IDEAS OF PROJECTION. 

10. In Projection Drawing, all objects are repre- 
sented by their -projections upon fixed planes of refer- 
ence. Hence an understanding of the geometrical 
meaning of the term ''projection " is essential. 

11. From Geometry we have : " The projection of a 
point upon a straight line is Va^foot of the perpendicular 
dropped from the point upon the line." 

Thus: 



A 



\ 



Q 



vlfi^yK. \ , 



13 



14 



MECHANICAL DRAWING. 



Let AB be any straight line, and P any point not in 
the line. Let Pp be perpendicular to AB. Then p is 
the projection of P upon the line AB, 

12. Similarly : " The projection of a point upon a plane 
is the foot of a perpendicular from the point to the plane. 

Thus : 



K 




P is a point in space, and Pp a perpendicular from P 
upon the plane ABCD. p \^t\i^ projection, then, of P 
upon the plane. 

13. The projection of any line, or surface, or solid, may be 
found by finding- the projections of all of its points. 
For lines and surfaces are but successions of points, 
and solids are bounded by surfaces. 

APPLICATION OF PROj:eCTION TO DRAWING. 

14. Now consider two mathematical planes of in- 
definite extent, intersecting- each other at rig-ht ang-les, 
fixed in position, one horizontal and the other vertical. 
Let the following- fig-ure represent limited portions of 
these two planes : 



APPLICATION OF PROJECTION TO DRAWING. 15 




f' 



to ur-e 



§. 



Let the vertical plane be denoted by Fand the hori- 
zontal plane by //, and their line of intersection by GL. 

15. Now imagine a point to be situated in space in 
one of the ang-les of these two planes, as shown in 



Fig-. 4 : 




Ptourc ¥. 



16 MECHANICAIv DRA\YING. 

Let P be the point in space in the angle of the two 
planes. 

Now froject P upon the horizontal plane, and then 
on the vertical plane. Then f> is the projection of P 
upon the horizontal plane, and f is the projection of P 
upon the vertical plane. 

Draw pm and ft'in perpendicular to GL, in the hori- 
zontal and vertical planes respectively. 

16. Now it can readily be seen that these -projec- 
tions of P upon the two planes, fix the position of P in 
space, exactly. For if f> and p' be known, P can be 
found at once by erecting* perpendiculars, which will 
intersect in the position of P. 

17. By means, then, of their projections upon two 
fixed planes^ points anywhere in space may be repre- 
sented. If points can be thus represented, lines and 
surfaces, and all objects, may be represented in the 
same way. 

18. Now, while by this means all g^eometrical 
quantities can be completely represented in space, no 
application can be made of this method until some 
means is provided for bringing everything into one 
plane, which can be made to coincide with the surface 
of a sheet of drawing paper. 

19. From Fig. 4 it is easily seen that all the quan- 
tities may be readily brought into one plane, and with- 
out destroying any of the essential relations. 

Imagine the vertical plane to revolve backward 
about its intersection, GL^ while the horizontal plane 
remains fixed. Let it revolve downward until it coin- 
cides with the horizontal plane, carrying its projection 
of the point with it to a new position p ' . 

20. Evidently all quantities will retain their same 
relations, and we may now deal with the revolved po- 
sitions of the point, and no longer consider the point. 



NOTATION. 17 

21. When the two planes have been made to coin- 
cide, they, with the projections of the point, may be 
broug-ht into the plane of the paper, and will appear as 
shown in Fig". 5 : 



G 



nt 



The line of intersection GL, is placed horizontal on 

the drawing", with the projections upon the vertical 

plane above, and those upon the horizontal plane below 

it. 

NOTATION. 

TERMS EMPLOYED. 

22. For convenience and brevity the following terms 
are used : 

(1) The two fixed planes are called " t/ic planes of 
projection,'' or '* the co-ordinate planes,"" or " the 
planes of reference.'''' 

(2j The vertical plane of projection is called simply 
""' the vertical pkoie,"" or commonly, " K." 

(3) The other is called '' the horizontal plane,'' or 
simply, *'//." 

(4) The line of intersection of the two planes is called 
'' the g-ro2ind line," or briefly, '' GL." 



18 MECHANICAL DRAWING. 

(5) The projection upon V {p\ Fig's. 4 and 5;, is 
called " t/ie vertical projection,'" or simply ''the V 
project i 0)1.'' 

(6) The projection upon H (/, Fig's. 4 and 5), is 
called ''the horizoiital projection,^' or " the H pro- 
ject ion.'' 

(7) The perpendiculars dropped from a point in space 
(^Pp and Pp\ Fig". 4), are known as projecting" lines. 
On the actual drawing-, Fig*. 5, pm and p ' in are com- 
monl}^ called the projecting- lines, thoug-h the}^ are 
reall}^ the projections of the projecting* lines. 

LETTERING. 

23. (1) Points in space are denoted b}^ a capital let- 
ter, as P, Fig-. 4. 

(2) Projections of points are lettered with the corre- 
sponding- small letters. 

(3) Vertical projections are alwa^^s primed. 

(4) Horizontal projections are not. 

(5) If a point in space be moved into several positions 
in succession, the same letter is used for all of the po- 
sitions. The successive positions of the V projection 
are denoted b}^ the same letter that is used for the first, 
marked with ^^ ^^^, ^^', and so on in order. The H pro- 
jections are marked with the corresponding- sub- 
scripts, o, 3, 4, &c. 

For example, if a point A should move successively 
to ^", ^4"\ A"^', &c., its V projections would be let- 
tered cC-, a^\ a^^\ a^^\ &c., and its H projec- 
tions a, a. 2, ((i, ct \. &c. 

(6) Projections of plane "fig-ures and all surfaces and 
solids, are lettered b}' selecting* prominent points on 
them, and lettering these according- to the system of 
lettering- points in g'eneral. 



GENERAIv PRINCIPLES. 19 

(7) Projections of particular angles are marked by 
small dotted arcs, and lettered with the minor letters 
of the Greek alphabet. But one letter is used to de- 
note an ang-le. The \ " /", &c., and subscripts, are 
used on letters marking- the projections of ang-les, just 
as on letters denoting* projections of points. 

GENE^RAI, PRINCIPLES. 

POINTS. 

24. By reference to Fig-. 4, the following- funda- 
mental principles are established in reg-ard to the pro- 
jections of points, on the actual drawing", where the 
two planes coincide, as in Fig*. 5: 

(1) The two projections of a point in space fall on a 
straig-ht line, which is perpendicular to the g-round 
line. The vertical projection is above, the horizontal 
belozv GL. 

(2) The distance of the vertical projection from the 
g-round line, is equal to the distance of the point from 
the horizontal plane in space. 

(3) The distance of the horizontal projection from 
the g-round line, is equal to the distance of the point 
from the vertical plane in space. 

LINES. 

25. As lines are made up of successions of points, 
any line may be represented by finding- the two projec- 
tions of all its points. These projections of the points 
constitute i\\.^ projections of t lie line. 

SURFACES AND SOLIDS. 

26. In general, the two projections of surfaces and 
solids may also be conside^xd as made up of the proiec- 
tions of all the points composing- them. 



20 MECHANICAL DRAWING. 

27. In the case of limited portions of surfaces, it is 
sufficient to consider simply the projections of the lines 
bounding them. 

28. In the case of solids, the projections of the 
bounding- surfaces only are necessary. 

29. Definite principles governing- the projections of 
lines, surfaces and solids, and special directions for 
particular cases, will be given as occasions arise for 
their use. 

POINT OF SIGHT. 

30. Consider the two projections of an object. It 
IS evident that either projection is just what would be 
seen by an observer looking at the object in a direction 
perpendicular to the plane of projection, if the eye 
were at an infinite distance from the plane, and en- 
dowed with correspondingly infinite power. 

31. The point of sight is thus assumed at an infinite 
distance so that the lines of sight will coincide with 
the projecting lines of the object. 

32. The vertical projection may then be considered 
as a side or front view of the object. And in the same 
way, the horizontal projection may be considered the 
^' top view." 

33. When the point of sight is assumed in this way 
at an infinite distance, the method of representation is 
known as OrthogTaphic Projection. 

34. When the point is at any position within finite 
distance, the method is known as Scenographic, and 
the resulting projection is called the Perspective of the 
object. 

35. Perspective views "d^x^ perfect pictures., but are 
not suitable for working drawings, as the dimensions 
of objects are not given by them in their true relation. 



DRAWING — CONVENTIONAIv LINES. 21 

DRAWING. 

CONVENTIONAIv LINES. 

Ordinary Full Line. 

36. The projections of lines in space, either g-iven 
or required, are drawn with an ordinary " weig'ht " of 
'"'' /ttll line.'' 

Auxiliary Line — Fine Full Line. 

37. Projections of lines that are auxiliary, — that is 
used simply as aids, — are drawn with full lines made 
enoug"h liner than the ordinary " full lines " to be in 
marked contrast with them. 

Construction Line. 

38. The two projections of all points are always 
joined with a " dotted line,'' made up of short dashes, — 
best about (^ of an inch long- and j^ of an inch apart, — 
of the weig'ht of the "fine full line." 

This is also used to indicate the paths of moving' 
points, as in cases of revolution, where the projections 
of points move from one position to another. 

Invisible Line. 

39. Projections of lines which are hidden from view 
by intervening- surfaces, are drawn with the " i)ivisible 
line," which is made up of dashes about g^ of an inch 
long-, and ^i of an inch apart, and of the weig-ht of the 
"fine fuUline." 

Gronnd Li)ie. 

40. The g-round line is drawn with a heav}^ full 
line, about twice the weig-ht of the ordinar}^ full line. 

ISOLATED POINTS. 

41. Projections of isolated points are marked with 
small fine crosses, as in Fii**. 5. 



22 MECHANICAIv DRAWING. 

D^XERCISB. 

42. Prepare a plate of specimens of the conventional 
lines to be used. Adopt lines of the proper "weight" 
and kind, and mark each line with its name. Leave 
space upon the plate for two or three additional lines, 
which will be met with later. 

Keep this plate for reference, and always make all 
lines according- to it. 

PROJECTIONS OF A POINT. 

43. The two projections of any point in space may 
he readily constructed directly from the fundamental 
principles in regard to projections of points — page 13. 

Plate I. 
Represent by their two projections the six points sit- 
uated as follows : 

(1) A point J " from Fand 1| " from //. 

(2) A point in F, and 1 " from H. 

(3) A point 1 " from F, and k " from //, 

(4) A point h " from F, and l\ " from H. 

(5) A point I " from F, and in H. 

(6) A point I " from F, and | " from H, 

Directions : Draw the ground line thro the plate 
a little below the middle, stopping it at equal dis- 
tances from the end border lines. Place the points 
so that their projecting lines on the drawing will be 
equal distances apart. Letter the projections correctly. 

Remark : For a plate 6^ '' by 8 Vz " with % '^ border, the ground 
line should be ^Yz'^ from the lower border, stopping Yz '^ from each 
€nd border line. 

PROJECTIONS OF I^INES. 

44. In general the projections of any line, curved or 
straight, may be found by projecting all of its points, 



PROJECTIONS OF RIGHT LINES. 23 

but ill reality all the points can never be projected. 

45. In the case of a curved line, a number of points are 
chosen, as near tog"ether as the accuracy of the work 
may demand, and their two projections found. The 
corresponding- projections of these two points are then 
joined by smooth curves, which are the projections of 
the curve in space. 

46. In the case of a straig^ht line, it is sufficient to 
simply project any two of its points, and then join the 
corresponding- projections of these points by straight 
lines. 

PROJECTIONS OF RIGHT LINES. 

47. The following- principles in regard to the pro- 
jections of right lines are of great importance. They 
may be easily verified by a consideration of the lines in 
space, situated according to the assumptions made. 
They should be illustrated by simple models. 

PRINCIPEES. 

(1) The projections of a line can never be longer 
than the line itself. 

(2) When a line is parallel to either co-ordinate plane, 
its projection on that plane is equal to the actual length 
of the line in space. Its projection on the other plane 
is parallel to the ground line. 

(3) If a line is parallel to both co-ordinate planes, 
it is parallel to the ground line, and both of its projec- 
tions are parallel to the ground line. 

(4) If a line is perpendicular to either co-ordinat^^^* 
plane, its projection on that plane is a straijj;Kl^^rine 
perpendicular to the ground line. "^ 

(5) If a line is oblique to one co-ordinate plane, but 
is parallel to the other, the projection on the plane to 
which it is parallel gives the true size of the angle 



24 MECHANICAL DRAWING. 

which the line in space makes with the plane to which 
it is oblique. 

Evidently, from the preceding, when a line is oblique lo both planes^ 
neither projection gives its true lengtJi, or the angle it makes with either 
plane. 

(6) If a point be in a line, or a line is to pass throug*h 
a g-iven point, the projections of the point must be on 
the projections of the line. 

(7) If two planes in space intersect, their projections 
intersect, and the two projections of the point of inter- 
section lie on a strai§"ht line, perpendicular to the 
gfround line. 

For the point of intersection is in both lines, hence its projections are 
on the projections of both, and therefore at their intersection. The 
point of intersection is simply a point, hence its projections are governed 
by the laws of points in general. 

(8) If two lines are parallel in space, their corre- 
sponding- projections are parallel. 

Principles (6) and (7) are equally true for lines in general, as well as 
for straight lines. 

Plate II. 

Construct the two projections of each of the three 
straig"ht lines situated as follows : 

(1) A line, CK, 1| '' in length, parallel to F, and 
parallel to H, 1| " above H, and \\" in front of T. 

(2) A line BH, 2" in length, parallel to H and in- 
clined to Fat an angle of 45°, the line to be Ig '' above 
H, and the extremity nearest F, h " from F. 

(3) A line FL, If " in length, parallel to F, and in- 
clined at an angle of 30° to H, \ " in front of F, and its 
lower extremity 1 " above H. 

Directions : Draw GL as before. Arrange the 
drawing to suit the plate. 

For standard 6|4f by 8>^ plates, the directions are : Place the first pro- 
jecting line y^^^ from the left border. Leave Yz^^ between the projecting 
lines of{i) and {2), and of {2) and ( j). 



REVOLUTION OF A POINT. 25 

RBVOI/UTION. 

48. It often becomes necessary to revolve points, 
and lines, and even entire fig-ures, in space, by means 
of their projections. Evidently, any object may be re- 
volved, if the principles g-overning" the revolution of a 
^oint are known. 

REVOLUTION OF A POINT. 

49. A point is said to be revolved about a straight 
line, as an axis, when it is so moved that it describes 
the arc of a circle, whose center is the axis, and whose 
plane is perpendicular to the axis. 

50. The angle through which the point is revolved, 
is measured by the arc described. 

51. It is evident, that when all points of a figure 
are revolved about an axis, and through the same 
angle, their relative positions remain unchanged. 

PRINCIPLES. 

52. The following are true in regard to the revolu- 
tion of points. They are readily verified by consider- 
ing the quantities in space : 

(1) If a point be revolved about an axis, perpendicu- 
lar to one plane of projection, its projection on that 
plane describes a circle arc. Its projection on the other 
plane moves in a straight line parallel to the ground 
line. 

(2) If the axis be parallel to one plane of projection, 
and oblique to the other, the projection of the point of 
the plane to which the axis is parallel, moves in a 
straight line perpendicular to the projection of the axis 
on that plane. The other projection describes an 
ellipse. 

It is a general rule that when the axis is parallel to one plane, however 
situated with respect to the other, that the projection of the point on the 
plane to which the axis is parallel, moves in a straight line perpendicular 
to the projection of the axis. 



26 MECHANICAIv DRAWING. 

PivATE III. 

I. Given the two projections of a point P, situated 
\%" above H, and | " in front of F, and an axis perpen- 
dicular to H, 1 " from the point, revolve the point about 
the axis through an angle of 75°, and find its projec- 
tions in the revolved position. 

II. Given the point M in space, situated | " above 
H, and \\ " from V. Revolve it, first about an axis 
perpendicular to F, \\ " from it, through an angle of 
90°, and then from this" position, about an axis perpen- 
dicular to H, I " from it, revolve it through an angle of 
60°, and construct its projections. 

Directions : Draw GL as before. Arrange the 
drawing to suit the plate. The axes being g-iven 
quantities^ will be drawn with full lines. Letter all 
the projections correctly. For the projections of the 
radius of revolution in each case, use the "dotted 
line " here. 

REVOLUTION OF LINES. 

53. When a straight line is oblique to both planes 
of projection, neither projection shows its true length, 
or the angle it makes with either plane. 

54. To find the true length of a line so situated, or 
the angles it makes with the planes of the projection, it 
is necessary to revolve the line. 

55. To revolve a straight line, it is only necessary to 
revolve any two of its points through the same angle, 
and join their revolved positions by a straight line. 
Whenever possible, the axis of revolution is assumed 
through some point of the line, — preferably one ex- 
tremity. Then it is only necessary to revolve one 
point, — usually, the other end. 



REVOLUTION OF PLANE FIGURES. 27 

Plate IV. 

Given the two projections of a line, the left-hand end 
of which is IJ " above H, and | " in front of F, and the 
rig*ht-hand end \ " above H, and 1| " in front of F, its 
H projection being* inclined 45° to GL. 

Find the true length of the line, and the angles it 
makes with Fand with H, 

Directions: Draw GL as before. Arrange the 
drawing in the middle of the plate. 

The assumed, •and derived projections, are g'iven and 
required, hence are drawn with the ordinary full line. 
The lettering must show the order of the steps taken. 

The projections of the axes of revolution, will not 
be drawn. They will be omitted hereafter. But they 
should be sketched for the study of problems. 

The ground line may be left unlettered hereafter. 

Plate V. 

Find the two projections of a line 1| '' long, situated 
so that its* left-hand end is | " above H, and 1^ " in 
front of F, and its right-hand end is If " above H, and 
1| " in front of F. 

Directions: Draw 6^Z as usual. Place the problem 
in the middle of the plate. 

Suggestion : It will be necessary to place the line first in an auxiliary 
position, 

REVOLUTION OF PLANE FIGURES. 

56. In the case of polygons, it is only necessary to re- 
volve their vertices, according to the principles of revo- 
lution of points in general. All points of a polygon 
must be revolved through the same angle. 

57. In the case of a plane curve, points must be as- 
sumed upon the curve as near together as the accuracy 
of the work demands, and these revolved, all thro the 
same angle, according to the rules for points in general. 



28 MECHANICAL DRAWING. 

Plate VI. 

Having' g-iven the two projections of a regular hex- 
agon, in space, parallel to V, two sides of the hexagon 
parallel to //, about an axis perpendicular to //", thro 
the left-hand extremity of the horizontal diameter, re- 
volve the hexagon thro an angle of 45°, and construct 
its projections. 

Then revolve it again about the same axis, till the 
plane of the figure inclines 60° to V. Revolve again» 
till the hexagon comes perpendicular id V. 

Directions: Draw (9Z as before. Let the diameter 
of the circumscribing circle of the hexagon be 2 " , 

Letter the projections of the vertices of the hexagon 
in all their positions. 

Plate VII. 

Having- given a circle 2 " in diameter, in space, paral- 
lel to H, about an axis perpendicular to F, tangent to 
the circle, revolve it downward until its plane is in- 
clined at an angle of 45° with H. Then assume an 
axis thro the center of the circle, perpendicular to H^ 
and revolve the circle about it through an angle of 30°. 

Construct the projections in both positions. 

Directions: Draw GL as usual. Arrange the 
drawing to suit the plate. 

PROJECTIONS OF SOLIDS. 

58. The projections of solids may now be readily 
constructed, from the principles of projection of lines 
and surfaces. 

Plate VIII. 

I. Construct the two projections of a right regular 
hexagonal prism, altitude 2\ " , radius of base | ", — the 
base of the prism parallel to H, and two faces of the 
prism parallel to V. 



SHADE LINES. 29 

II. Revolve the prism thro an ang"le of 30° to the 
right, keeping- one point in the base at the same height 
above H, and the two faces parallel to F. 

Construct the projections in the revolved position. 

Directions: Draw 6^Z whenever necessary to allow 
space for the constructions. 

Transfer the projections of the revolved position to 
the right of those of the first, to avoid confusion. 

SHAD^ LINES. 

59. On drawings of solid objects, it is customary to 
indicate by means of ''shade lines'' the surfaces on 
which light falls, and on which no light falls. 

CONVENTlONAIv DIRECTION OE EIGHT. 

60. The light is assumed to come always from over 
the left shoulder of the observer, in parallel straight 
lines, in the direction of the body diagonal of a cube, 
situated with two of its faces parallel to F, and two 
parallel to H, 

61. The projections, then, of a line, or " ray " of 
light, both make angles of 45° with the ground line. 

DEFINITION OE SHADE EINES. 

62. The projections of all lines of an object, which 
separate light from dark surfaces, are shade lines. 

63. They are drawn with heavy lines, of the weight 
used for the ground line. 

64. Shade lines, properly placed, add greatly to the 
appearance of a drawing, and make it easier to under- 
stand or " read." 

65. The shade lines of a drawing are, in most cases, 
easily determined by considering the direction of light, 
and how the rays must strike upon the object repre- 
sented. In some instances, however, it is difficult to 



30 MECHANICAL DRAWING. 

decide which should be shade lines, without a knowl- 
edge of the methods of finding- the shadows of objects. 
It is, however, rarely difficult in ordinary mechanical 
drawing-, to determine the shade lines. 

EXERCISE. 
66. Place the proper shade lines on the projections 
of Plate VIII. 

Peate IX. 
Construct the two projections of the following- : 

(1) A rig-ht regular hexagonal pyramid, base paral- 
lel to H^ two edges of the base parallel to V, — radius 
of base | '\ altitude of the pyramid 2\ " . 

(2) A right circular cylinder, axis perpendicular to 
H, diameter 1^ ", altitude 2\ ". 

(3) A right circular cone, axis perpendicular to H, 
diameter of base 1\ " , altitude 2J " . 

Directions : Place all three objects the same height 
above H^ and with their axes the same distance from 
F. 

Place the proper shade lines. 

Plate X. 
Construct the two projections of the following : 

(1) A sphere 2 " in diameter, situated in space. 

(2) A prolate ellipsoid of revolution, major axis 
2J " , minor axis \\ ", 

Directions : Arrange the drawing to suit the plate. 
Decide in regard to shade lines. 

Note. An ellipsoid of revolutio7i is generated by revolving an ellipse 
about one of its axes. If about the major axis, a prolate ellipsoid is gen- 
erated, — if about the minor axis, an oblate ellipsoid. 

THIRD PROJECTION. 

67. In certain special cases, the usual two projec- 
tions do not completely represent an object. For in- 



THIRD PROJECTION. 31 

stance, if a cylinder should lie with its axis parallel to 
the ground line, the H and V projections would not 
represent it, as they would not then be different from 
the two projections of a square ^rism similarly situated. 

68. In every such case a third projection is neces- 
sary. This is obtained as follows : 

69. A plane is "passed" perpendicular to both H 
and F, in any convenient position, just to the rig-ht of 
the object to be represented. 

70. This plane is indicated by the lines in which it 
intersects ^ and V, These lines are called "traces," 
and are drawn with a line made up of a dash and three 
dots repeated, — the dashes about 3_ " long-, and of the 
weig"ht of the full line, — the dots like those of the con- 
struction line, — which is the Descriptive Geometry 
symbol for "Auxiliary Plane Trace." 

71. This plane is known as the *' profile plane." Hav- 
ing- the third co-ordinate plane, the object is projected 
upon it, and it is revolved to the right about its ver- 
tical trace until it coincides with V. Then V is re- 
volved down as usual, carrying- the projection of the 
profile plane with it. 

72. By means of these three projections, every pos- 
sible geometric figure can be represented completely. 

SHADE LINES. 

73. Shade lines on the third projection are arbitra- 
rily placed, just as they are in the vertical projection. 

Plate XI. 

Construct the projections of a hollow cylinder, out- 
side diameter \\ ", inside diameter \" , length 2A ", sit- 
uated with its axis parallel to H and to \\ | " in front 
of F, and \\ " above H. 

Directions : Draw the ground line wherever neces- 
sary. Arrange the drawing to suit the plate. 



32 MECHANICAL DRAWING. 

For the standard 6\^ " by SJ2 " plate, CL should be 2}^ " above the 
lower border- 

REVIEW QUESTIONS. 

Q. S. What is Projection Drawing ? 

Q. 9. Its methods are those of what scienee ? 

Q. 10 Of what great branch of mathematics is Orthographic Projec- 
tion the basis ? 

Q. II. In Projection Drawing, how are objects represented ? 

Q. 12. What is the "projection" of a point upon a line? 

Q. 13. Urcr a rla-e? Illustrate. 

Q. 14. E : " : ~ : - 1 ; r : r : : : - of a line found ? 

O- 15. O:' a =ur:£Cc : O: a. solid? 

O. 16. How may two projections of a point be made to £^x the posi- 
tion of the point in sp a;e - 

Q. 17. Howare:"::e : -_sr'. p'atirs a^su—e". :: ':e situated in space ? 

Q. iS. If points are rxei : Litir : v: pre t::.:::-, ~ay 1 ne; :e also? 

Q. 19. And surfaces, and so'.ii fr-res - 

Q. 20. Can any use be made of this r:e:'::: i ::' represeutatiru. with 
the planes actually at right angles? 

Q. 21. What is ueiei ary in order that application may be made of it? 

Q. 22. H-vi~ li- rehire" eut met ^ 

Q- 23. Will the f^vj projections hx a point as well wheu the twc 
planes are maie to cclncide? 

Q. 24. How is the plane figure resulting from bringing the two planes 
into coincidence, placed on the drawing? Make a sketch showing the 
two projections of a point. 

Q 25. What are the two fixed planes called ? 

Q. 26. What is the name of the vertical plane ? 

O. 27. Of the horizontal ? 

Q. 28. Of the line of their intersection ? 

Q, 29. What is meant by the //"projection of a point? 

Q. 30. The J ' projection ? 

Q. 31. What are projecting lines ? 

Q. 32. How are the projections of a point lettered? 

Q 33. How are the projections of the successive positions, P, P'\ 
P"\ pi-^ Slc , of a point, lettered ? 

Q. 34- How are the projections of plane figures lettered ? 

Q. 35. Of solids ? 

Q. 36. How are projections of imp>ortant angles marked? 

Q. 37. How are the two projections of a point always situated with 
respect to the ground line ? 

Q. 38. How is the distance of a point from H shewn ? 

O. 39. Which projection shows the distance of a point in space 
from r? 



REVIEW QUESTIONS. 33 

Q. 40. How may the projections be considered as " views ? " 

Q, 41. Which projection is the top view ? 

Q. 42. What is the difference between orthographic and scenographic 
projection ? 

O. 43 What is the scenographic projection of an object commonly 
called ? 

Q. 44. What are conventional lines ? 

Q. 45. What are the ones used in Projection Drawing ? 

Q. 46. How are the projections of curved lines found ? 

Q. 47. Of straight lines ? 

Q. 48. Can the project of a straight line be longer than the line itself ? 

Q. 49. When will the projection equal the line ? 

Q. 50. If a line is parallel to one plane and oblique to the other, what 
is known regarding the projections ? 

Q. 51. Which projection gives the angle with the plane to which it is 
oblique ? 

Q. 52. If a line is parallel to // and V, how are its projections 
situated ? 

Q. 53. If a line is perpendicular to one plane, what is its projection 
on that plane ? 

Q. 54. What is its other projection, and how situated ? 

Q. 55. If a point be on a line, straight or curved, how are the projec- 
tions of the point and line situated with respect to each other ? 

Q. 56. If two lines, straight or curved, intersect, what is known of 
their projections ? 

Q. 57. If two straight lines are parallel in space, what is known of 
their projection^ ? 

Q. 58. When is a point said to be revolved about a straight line as an 
axis ? 

Q. 59. How must all points of a figure be revolved, not to change the 
figure ? 

Q. 60. If a point moves about an axis perpendicular to //, how does 
its V projection move ? 

Q. 61. What is the general statement of the principle ? 

Q. 62. How does the projection of the point on the plane to which the 
axis is parallel move, in all cases, whether the axis is perpendicular to 
the other plane or not ? 

Q. 63. Of what use are the principles of revolution ? 

Q. 64. How is a straight line revolved ? 

Q. 65. How is the true length of a line, oblique to both planes, found ? 

Q. 66. If a line is inclined to both // and F, how is its angle with f/ 
found ? 

Q. 67. How would a polygon in space be revolved ? 

Q. 68. Any curve ? 

Q. 69. For what are shade lines used ? 



34 MECHANICAL DRAWING. 

Q. "o. What is the conventional direction of light ? 

Q. 71. Are the rays of light assumed to be parallel ? Why ? 

Q. 72. How are the projections of a ray of light inclined to the ground 
line ? 

Q. 73. What lines are shade lines ? 

Q. 74. How are they drawn ? 

Q. 75. Of what use are shade lines ? 

Q. 76. How are shade lines determined on a drawing ? 

O. 77. Do two projections of all objects always represent them 

complete ? 

Q. 78. What is a notable instance ? 

Q. 79. What is done when the usual two projections are not sufficient ? 

Q. 80. How is the third plane passed ? 

Q. 81. When the projection has been formed on it, what is done with 
it? 

Q. 82. How is this third plane shown on the drawing ? 

O. Ss. What is the kind of line used for the "traces ?" 

Q. 84. What is the third plane called ? 

Q. 85. Can everything be completely represented by three projections ? 

Q. 86. How are shade lines placed on the third projection ? 



ISOMETRIG :flND OBLIQUE DIMVIN6. 



isom:etric. 

DEFINITION. 

74. Isometric Drawing is a method of representing" solid 
objects so that their three principal dimensions will be 
shown in their true values by means of but one view. 

75. An isometric drawing- of an object is an approx- 
imate -picture of it, which, unlike a true perspective 
view, shows the leng*th, breadth and thickness in their 
correct values. 

ISOMETRIC PROJECTION. 

76. Consider a cube in space, in the angle of the 
two planes of projection, with its base parallel to the 
horizontal plane, and one diag*onal of the base parallel 
to the vertical plane. 

77. Now let the cube be revolved forward from the 
vertical plane, about an axis parallel to the g*round line 
coinciding- with the diag-onal of the base, until a body 
diag-onal of the cube comes perpendicular to the vertical 
plane. 

78. It is readily seen now, that in this position the 
vertical projection of the edg-es of the cube, which are, 
of course, all equal in space, will be equal. For, all 
the edg-es make equal ang-les with the diag-onal, or its 
direction, which is perpendicular to \\ and hence equal 
ang-les with V. Hence V projections are equal. 

79. This F projection is the Isometric projection of the 
cube. 

3S 



36 MECHANICAL DRAWING. 

ISOMETRIC DRAWING. 

80. In the isometric projection of a cube, the pro- 
jections of the edg-es are all less, of course, than the 
edg-es themselves in space ; but all the edges are 
equally "foreshortened," — that is, the projections are 
prof)ortional to the edges themselves. 

81. All the projection of the edges may, then, be 
multiplied by a certain constant, and then will result a 
drawing on which the lengths of the edges of the cube 
are given exactly. 

82. This drawing is called the " Isometric drawing " of 
the cube, as distinguished from the Isometric projection. 

83. To make an isometric drawing of a cube, the true 
lengths of the edges are simply laid off in their proper 
directions on the drawing. 

84. These directions are known from the consider- 
ation that the projections of the edges must form a 
reg-itlar hexagon with its diagonals. 

85. All lines, then, are either vertical or inclined to 
the horizontal at angles of 30° either way. 

86. Now, it is evident that not only cubes, but 
all rectangular objects as well, may be represented by 
isometric drawings. 

87. For, any rectangular object may be placed with 
its edges parallel to those of the cube. Then they will 
have the same directions on the drawing as those of 
the cube, and will be equally " foreshortened," just as 
are the edges of a cube. 

88. These edges may be considered parallel in space 
to three rectangular axes. These axes will have fixed 
directions on all isometric drawings, — one vertical, one 
inclined 30° one way, and the other 30° the other wa3^ 

89. They are called the isometric axes. 



ISOMETRIC DRAWING. 37 

90. All lines of an object: parallel to these axes, are 
known as Isometric Lines. 

91. All dimensions parallel to isometric lines, are 
measured off their true length on the drawing-. 

92. Measurements not parallel to isometric lines, 
cannot be laid oif in their true values on the isometric 
drawing*. 

93. Isometric drawing is best adapted to representing- ob- 
jects made up of plane surfaces, and whose principal 
lines are parallel to the three rectang-ular axes. 

94. In almost all other cases there is g-reat distortion 
of the picture. 

95. It is, however, sometimes necessary to repre- 
sent non-isometric lines, and to draw curves isomet- 
rically, and to represent special points on an isometric 
drawing-. 

USE OF CO-ORDINATES. 

96. In all such cases it is necessary to have first 
the orthog-raphic projections of the object. Prom these 
the three rectang'uiar co-ordinates of any point of the 
object may be found, referred to some point that can 
be represented easily, and these then laid oif on the 
drawing". 

97. That is, the location of any -point may be deter- 
mined by measurements along- isometric lines from 
some point that can be shown isometrically. 

EXAMPivE. 

98. The use of co-ordinates in g-eneral is illustrated 
by an example in Pig*. 6, which is a simple timber joint. 
Evidently, the horizontal timber can be easily drawn 
in isometric, but the lines of the inclined piece and the 
joint are non-isometric. 



38 



MECHANICAL DRAWING. 




99. A single projection is sufficient here. From it. 
Fig-. 6, get the " co-ordinates " Oa and ad of point Ij; 
and Od and dc of any point C of the edge J^/I. 

Construct the isometric drawing of the horizontal 
piece OS. Then along OG on the drawing, la}^ off 
Oa from O, and from a downward lay off ad. This 
gives the lines I^d and bl^, as 7^ and 7? are on the iso- 
metric line and can be laid off at once. 

Next, to get the inclination of the other piece, lay off 
Od from O along OG, and upward lay off dC. Then 
there are two points determined and J^H C3,n be drawn. 

RK\^ parallel to FH on the object, hence will be on 
the drawing. 

The widths of the pieces are shown as usual. In 
this way the complete isometric drawing is. readily 
constructed. 

100. By a similar use of co-ordinates obtained from 
the ordinary projections, the isometric drawing of any- 
thing may be constructed. 

SHADE EINES. 

101. Shade lines are placed in isometric drawings 



ISOMETRIC DRAWING. 39 

according" to the same principles as in ordinary 
projection. 

DIRECTION OF LIGHT. 

102. The conventional direction of lig-ht is as be- 
fore, from over the left shoulder, in the direction of 
the body diag-onal of a cube. But here, this diag-onal 
is inclined downward and to the rig-ht at an angle of 
30° with the horizontal. 

103. Hence the direction of light on an isometric draw- 
ing-, is 30° downward to the right. 

PeatE XII. 
Represent by isometric drawing, 

(1) A cube with edges 1^ " . 

(2) An H shaped object formed from a cube 1| ''oe©''^^^ 
square, by cutting channels into tw^o opposite i::ftLl0fe^of 

the cube, and square m section. 

Directions : Arrange in the middle of the plate. 
Place the shade lines properly. ^ 

Peate XIII. 
Construct an isometric drawing of the model of a 
timber joint, shown in Pig 6, using these dimensions : 
Let OG=S". 
OM=l". 
Width, 0W=\", 
0F= \\ ". 
FH=Z\". 
HK=. OM^ I ". 

Fd ^ 

bFII^A right angle. 

Direclions: Place the drawing to suit the plate. 
Show the proper shade lines. 



40 MECHANIC AIv DRAWING. 

OBlvIQU^ DRAWING. 

104. Oblique Drawingf is very similar to Isometric. 
The only difference is that in oblique drawing- one of 
the axes, which in isometric is inclined at SO'', is made 
Jiorizontal, and all lines parallel to it. 

105. The lines that are inclined, may make any 
angfle with the horizontal, as well as 30°, and may in- 
cline to the left or to the rig-ht. 30° and 45° are com- 
monly used, preferably 45°. 

SHADE IvINES. 

106. Shade lines are determined as in Isometric 
Drawing-. When the inclined lines are to the rig-ht, 
the shaded lines are situated on an object just as on 
the isometric drawing- of it. But when the lines incline 
to the left, they will be different, for the lig-ht must 
come in such a way as to make the front face illumi- 
nated ; that is, the lig-ht cannot come from the rear, 
hence all the illuminated faces of a cube or prism, or 
other rectang-ular object, will be visible. 

CABINET PERSPECTIVE. 

107. Cabinet Perspective is a common term for Oblique 
Drawing-. In this, the inclined lines are drawn at an 
ang-le of 45° to the right. 

PI.ATE XIV. 
Represent in Oblique Drawing-, 

(1) A cube \\ " square, making- the inclined lines on 
the drawing- 30° to the rig-ht. 

(2) The same cube, making- the inclined lines 60° t3 
the rig-ht. 

Directions : Place the shade lines properly. 

Peate XV. 
Represent in Oblique Drawing-, 



REVIEW QUESTIONS. 41 

(1) A cube 11 " square, making* the inclined lines 
45° to the left. 

(2) A cube 11 " square, making- the inclined lines 
45° to the rig-ht. 

Directions : Place the shade lines properly. 

Compare the four drawing's of this cube in Plates 
XIV and XV, and decide which represents the cube 
best. 

EXERCISE. 

Represent in Cabinet Perspective the timber joint of 
Plate XIII, using- the dimensions there g-iven. 

REVIEW QUESTIONS. 

Q. 87. What is Isometric Drawing ? 

Q. 88. How does an isometric drawing differ from a perspective 
view ? 

Q. 89. How is the isometric projection of a cube obtained ? Illustrate. 

Q 90. Why is it that the projections of the edges are all equal ? 

Q. 91. What kind of a figure is then formed by them ? 

Q. 92. How is the isometric drawing derived from the isometric 
projection ? 

Q. 93. Why is it allowable to multiply all the edges by the same 
thing ? 

Q. 94. How is an isometric drawing of a cube actually made ? 

Q. 95. What directions have the edges on the drawing ? 

Q. 96. How is it known ? 

Q. 97. Can isometric drawings be made of anything but cubes ? 

Q. 98. Why ? How ? 

Q 99. What are the isometric axes ? 

Q. 100. What are the isometric lines ? 

Q. loi. What dimensions may be measured off on an isometric 
drawing ? 

Q, 102. Why cannot others ? 

Q. 103. For what are isometric drawings best adapted ? 

Q. 104. How are isometric drawings of curves and non-isometric lines 
in general, drawn ? Explain and illustrate. 

Q. 105. How are shade lines determined in isometric drawing ? 

Q. 106. What is the conventional direction of light ? 

Q. 107. What is the direction of a ray on the drawing ? 

Q. 108. How does Oblique Drawing differ from Isometric. 



42 MECHANICAL DRAWING. 

O. 109. What are the usual directions for the axes in Oblique 
Drawing ? 

O. no. How are shade lines determined in Oblique drawing ? 

Q. III. Do the shade lines of a cube come on the same edges when it 
is shown with the inclined lines to the left, as when they are to the right ? 

Q. 112. Why is this so ? 

Q. 113. What is Cabinet Perspective ? 

Q 114. Why so called ? 

Ans. Because it is an approximation to true perspective, and was in- 
tended to be especially useful to cabinet makers. 

Q. 115. What are the directions of the principal lines in Cabinet 
Perspective ? 



WORKING DIMWINGS. 



108. The object of a working drawing is, briefly, to show 
the workman what to make and hozu to make it. 

109. Working" drawings are made in accordance 
with the principles of projection, but the rig-id laws, 
and the refinements and conventionalities of Projection 
Drawing, are not strictly observed. They are made in 
the simplest and best way to accomplish the object for 
which they were intended. 

THE THREE VIEWS. 

110. Usually the ordinary three projections are 
employed, situated in their customary relation to each 
other. 

111. The vertical projection is called simply the 
elevation, or the "front" or '*side view." 

112. The horizontal projection is called the Plan, or 
*' top view." 

113. The third projection is called the second elevation, 
or "end elevation," or simply "end view," — in some 
cases, "side view." 

114. In some cases two end views are needed. The 
view from the left is drawn to the right of the eleva- 
tion, and the view from the right to the left of it. 

115. When the views are not placed in their usual 
relation, they must each be plainly marked. 

SECTIONS. 

116. In very many cases a better idea can be given 
the workman of the shape and dimensions of an object, 

43 



44 MECHANICAL DRAWING. 

if it is cut thro in some way by a plane, and the cut 
surface drawn. Such drawings are called "sectional 
views," or "sections." 

117. Sections are used to show interiors of hollow 
objects, and in all cases where the clearness of the 
drawing will be increased. 

118. Sectional views are arranged in convenient relation 
to the other views. The best way of taking sections 
and arranging the views, varies with each particular 
case, and can best be learned by practice. 

119. In many cases, pieces are better sectioned half 
way thro, and the other half left as a simple view. 

120. In very many other cases, it is sufficient to pass 
a cutting plane only a little way, and then break out a 
piece to disclose some special feature. 

121. As a rule, cutting planes are passed parallel to 
the planes of projection whenever possible. 

CROSS SECTIONING. 

122. In every sectional view, %v her ever material is 
cut, the cut surface is ' ' sectioned ' ' with fine lines 
spaced equal distances apart, inclined 45° to the hori- 
:Eontal. 

123. The spacing will vary with the size of the draw- 
ing, being finer for small drawings than for large ones. 

124. Cut pieces adjoining on the drawing, should 
be sectioned in opposite ways. When it is impossible 
to avoid sectioning two adjacent pieces in the same 
direction, the ruling should offset. And the smaller 
piece may be sectioned finer than the other. Thus 
there is never any cause for confusion. 

Note : Some favor the use of 30° and 60° lines for sectioning, when 
there are several cut surfaces adjacent. This is not necessary, however, 
and is not so good. 

125. Formerly there was a particular kind of cross 
sectioning employed for every different kind of material. 



GENERAlv RULES. 45 

It is usual now, and much better, to mark each piece 
by means of reference letters, or in words, to show the 
kind of material to be used. This can be done for 
pieces not sectioned, as well as for those that are. 
There is no chance then for mistakes due to ig'nor- 
ance of the conventionalities on the part of the 
workmen. 

126. No set of fixed rules can be laid down for 
making" working" drawings, but a few g'eneral directions 
should be observed. 

127. The views to be shown, of an object, the man- 
ner of arranging- them, and the character and finish of 
the drawing, are all largely matters of judgment on 
the part of the draftsman in each instance. He must 
be guided by the purpose for which the drawing is in- 
tended, and by the best practice. 

128. On working drawings, "ground line" is 
generally omitted. It is well to use it in drawings of 
small pieces. 

129. The "projecting lines," also, are never used 
except on drawings of small pieces, and in cases where 
the use of a few of them will add to the clearness of 
the drawing. 

130. Drawings are lettered only when necessary for 
reference, and then simply in whatever way may seem 
best in the particular case. 

SHADB I^INISS. 

131. Shade lines should always be placed on work- 
ing drawings according to the rules of Projection 
Drawing. Shade lines correctly placed, add greatl3% 
not only to the appearance of a drawing, but also to 
the ease with which it may be used. 



46 MECHANICAL DRAWING. 

132. Shade lines are determined for sectional views 
in the same way as for other views. 

DRAWING TO SCAI<B. 

133. All drawings should be "made to scale," so 
that the dimensions on the drawing will bear a fixed 
ratio to those on the object represented. 

134. The best scale to adopt, is a matter of judg- 
ment in each particular case, and depends on the size 
of the drawing desired, and the peculiarities of the 
thing represented. The scale should be chosen so that 
the drawing will not be unnecessarih^ large, and yet 
large enough to show the details of the thing repre- 
sented, clearh'. The scale adopted should be noted on 
the drawing, as, IJ "= 1 '. 

DIMENSIONING DRAWINGS. 

135. Altho drawings are made to scale, all important 
dimensions must be clearlv marked on the drawinsf in 
figures. It is verv important that the figures be per- 
fectly distinct. Feet are indicated by the prime mark 
(0, and inches by the seconds '"). 

136. Dimensions that are horizontal, or nearly so, 
read, of course, from left to right. Dimensions that 
are vertical, must read from bottom to top. 

137. The exact point, or lines, between which the 
figures Sfive the measurements, are indicated bv a line 
called the "dimension line," drawn between them. 

138. The following is used as the dimension line, 

— , a neat "arrowhead" being placed at 

each end, the line being broken out for the figures. 
The length of the dashes used, varies somewhat with 
the size of the drawing and the use to be made of it. 

139. The placing of the dimensions on a drawing, 
is a matter requiring considerable attention. Every 



CENTER IvINES. 47 

necessary measurement must be g^iven, but g^iven only 
once. 

The "over all" dimension should always be given ^ 
and in close relation to those of the parts. 

Care must be taken not to confuse a drawing- with 
the fig"ures or the dimension lines. 

CENTER IvINE. 

140. It is often necessary to use a "center line.'^ 
Its uses will be learned by practice, as necessity for it 
occurs. It would be drawn, for instance, in the draw- 
ing* of a shaft and pulleys, thro the center of the shaft. 
In the plan of an engine, it would be drawn thro the 
center of the shaft and also thro the center of the 
cylinder, perpendicular to the shaft. 

141. The line used is like the dimension line, but 
made up of a dash and tvjo dots repeated. 

142. The center line is also used to indicate the 
location of a section. It is drawn where the cutting 
plane is imagined to be passed. 

ISOMETRIC AND OBI^IQUB FOR WORKING 
DRAWINGS. 

143. Isometric and oblique drawings are not customarily 
used for working drawings. They may be used, how- 
ever, for simple things. They are well suited for 
working drawings of simple rectangular objects, 
but are not generally used. Their principal use 
is for purposes of illustration. They serve to make 
doubly clear anything that may be difficult to under- 
stand from the ordinary working drawing. The}^ are 
helpful to those who are not very ready in reading- 
regular working drawings. In such cases, they ac- 



48 MECHANICAL DRAWING. 

company the reg"ular working* drawing's, and are not 
dimensioned. 

GENBRAI, VIEWS AND Dl^TAIIv DRAWINGS. 

144. A drawing- showing- all the parts of a machine 
or other structure, put tog-ether in their proper places, 
is called the "g-eneral drawing-," or "g-eneral view." 

145. When a machine is being- desig-ned, g-eneral 
views are made, usually plan, elevation, and second 
elevation, and sometimes sections. These show all the 
pieces in their proper relations to each other, drawn to 
scale, so that the desig-ner is able to adapt them to each 
other, and decide upon their dimensions. 

DETAILS. 

146. These g-eneral drawing's are usually too much 
crowded and confused to allow the dimensions of all 
the pieces to be placed on them, so that the mechanic 
can work from them. 

147. Each piece must be picked out from the g-eneral 
drawing-, and a separate and larg-er drawing- made of 
it to scale, with the dimensions all fig-ured. These draw- 
ing-s of the pieces are called *' Detail Drawings," or 
*' Details." 

148. In cases where much machine work is to be 
done on the pieces, a set of details is made for the pat- 
tern maker, and another set, showing- the dimensions of 
the finished pieces and the machine work required, is 
made for the machinist. The instructions to both the 
pattern maker and the machinist, may often be shown 
on one drawing-. 

149. Detail drawings are made in pencil on ordinary 
paper, preferably "detail paper," and then tracing-s 
made, which may be preserved. Prints are made for 
the workmen. 



GENERAL VIEWS AND DETAIL DRAWINGS. 49 

INDEXING. 

150. Details of complicated machines must be plainly 
marked, and numbered and indexed according- to some 
system, so that the tracing* of any detail may be readily 
found. 

151. Further knowledg^e of the endless variety of 
methods followed by draug^htsmen in making* working* 
drawings can only be acquired by prolong*ed practice 
under the direction of some one competent to instruct. 
In time, the ^'' idea'" of it all will become so instilled 
into one that he can work out ways for himself to fit 
any case he may be called upon to handle. 

RBVI:EW QTJiESTIONS. 

Q. ii6. What is the object of working drawings ? 

Q. 117. How are working drawings made ? 

Q. 118. Are any rigid set of rules followed strictly ? 

Q. 119. What is to guide then, in making a working drawing for a 
particular purpose ? 

Q. 120. What is the common name for the vertical projection ? 

Q. 121. For the horizontal projection ? 

Q. 122. When two end views are needed, how are they placed ? 

Q. 123. Is it allowable to place the views in any other relation ? 

Ans. Yes, if desirable for any special reason. Each view may be on a 
separate sheet, if necessary. (See Sec. 115.) 

Q. 124. What are sections ? 

Q. 125. For what are they used ? 

Q. 126. How should the cutting plane be passed ? 

Q. 127. Can any fixed rules be given for taking sections ? 

Q. 128. What is to guide, then ? 

Q. 129. How are cut surfaces shown on a drawing ? 

Q. 130. How is cross sectioning done ? 

Q. 131. Are there any fixe' rules that can be laid down for making 
working drawings, to cover all cases ? 

Q. 132. Why ? 

Q- 133- What are some general rules that should be observed ? 

Q. 134. Are shade lines used on working drawings ? 

Q. 135. How are the shade lines determined for sections ? 

Q. 136. What governs the choice of the best scale for a drawing ? 

Q. 137. What are some rules to be observed in dimensioning drawings? 



50 MECHANIC AIv DRAWING. 

What is the conventional dimension line ? 

For what purposes is a center line used ? 

What is the conventional center line ? 

Are isometric and oblique drawings used as working drawings ? 

Are they suitable for working drawings ? 

How are they generally used, when at all ? 

What is meant by a general view ? 

When is such a drawing required ? 

What are detail drawings ? 

How are detail drawings usually prepared ? 

How can it be arranged so that the shop drawing of any par- 
ticular detail of a large complicated machine may be readily found ? 

Q. 149. What may be said of acquiring familiarity with the many lit- 
tle "ways" of practical draughtsmen ? 



Q 


138. 


Q 


139- 


Q- 


140. 


Q. 


141. 


Q. 


142. 


Q. 


143. 


Q- 


144. 


Q 


145. 


Q- 


146. 


Q. 


147. 


Q 


148. 



ERRATA. 

1. Page 22, Section 43 : The reference should be to page 19, instead 
of 13. 

2. Page 23 : Sub-section [4) should read as follows : 

*' (4) If a line is perpendicular to either co-ordinate plane, its projec- 
tion on that plane is a point, and its projection on the other plane is a 
straight line perpendicular to the ground line." 

3. Page 24, sub-section (7) : For " two planes in space, " read "two 
lines in space. " 

4. Page 25, section 49 : Vox " whose center is the axis," read 
" whose center is in the axis." 

5. Page 29, Directions : For " whenever," read " wherever." 

project," read " projection," 
moves," read ** revolves." 

For " Complete," read " completely." 

9. Page 35, section 78 : The last sentence should read, " Hence 
their V projections are all equal." 

10. Page 36, section 81 : In the first line, for " projection," read 
'' projections." In the second line, for " then," read " there." 

1 1 . Page 38, section 99 : For dc read dC. 

12. Page 39 : Problem (2), under Plate XII, should read as follows : 
"(2) An H~shaped object formed from a cube i^ ^' square, b)- cut- 
ting channels into two opposite faces of the cube, the channels to be 
one-third of the width of the cube, and square in section." 

13. Page 40, section 106: For "shaded lines," read "shade lines." 

14. Page 41, O. 100: Omit "the." 

15. Page 45, section 128 : Insert "the" before " ground line." 

16. Page 45 : The last word on the page should be "read," instead 
of "used." 



6. 


Page 33, Q. 


48: 


P'or 


7. 


Page 33, 0. 


60: 


For 


8. 


Page 34, Q. 


77: 


For 



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